Model selection criteria Bayesian score: posterior probability P(mD P(mD)=P(mP(D m)/P(D) =P(m)P(DIm, e) P(e m)de/P(DI BIC Score: Large sample approximation of bayesian score BIC(m D)=log P(D/m, 8-d/2 logN d: number of free parameters; n is the sample size 8*: MLE of 0, estimated using the Em algorithm Likelihood term of bic Measure how well the model fits data Second term Penalty for model complexity. The use of the bic score indicates that we are looking for a model that fits the data well, and at the same time, not overly complex AAAl2014 Tutorial Nevin L Zhang HKUSTAAAI 2014 Tutorial Nevin L. Zhang HKUST 6  Bayesian score: posterior probability P(m|D) P(m|D) = P(m)P(D|m) / P(D) = P(m)∫ P(D|m, θ) P(θ |m) dθ / P(D)  BIC Score: Large sample approximation of Bayesian score BIC(m|D) = log P(D|m, θ*) – d/2 logN  d : number of free parameters; N is the sample size.  θ*: MLE of θ, estimated using the EM algorithm.  Likelihood term of BIC: Measure how well the model fits data.  Second term: Penalty for model complexity.  The use of the BIC score indicates that we are looking for a model that fits the data well, and at the same time, not overly complex. Model Selection Criteria